It's the majority, but overwhelming or not surprisingly appears to depend on car model, at least per some calculations someone on reddit ran [1].
I'd add though that rolling resistance tends to be higher, on average, in winter too. When there's often a bit of snow on the roads... Less so on high speed highways admittedly.
For most cars driving through air, at sea level, on planet Earth, at normal speed, the drag force F is proportional to the square of the speed (v^2).
That's not exponential because the speed (v) is not in the exponent. In fact, it's quadratic.
Corollaries: The power required to push the car at speed v will be proportional to Fv ~ v^3. The gas spent over time t ~ energy spent ~ power time ~ v^3 * time.
Define ‘high speeds’. There’s a reason race cars look like they do, to the point of having serious problems driving at speeds just a bit below highway speed limit.